Question: Solve for $x$ and $y$ using elimination. ${3x+2y = 7}$ ${4x-2y = 0}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $7x = 7$ $\dfrac{7x}{{7}} = \dfrac{7}{{7}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {3x+2y = 7}\thinspace$ to find $y$ ${3}{(1)}{ + 2y = 7}$ $3+2y = 7$ $3{-3} + 2y = 7{-3}$ $2y = 4$ $\dfrac{2y}{{2}} = \dfrac{4}{{2}}$ ${y = 2}$ You can also plug ${x = 1}$ into $\thinspace {4x-2y = 0}\thinspace$ and get the same answer for $y$ : ${4}{(1)}{ - 2y = 0}$ ${y = 2}$